Willie Nelson and Lyle Lovett sing together at the “Austin City Limits” Hall of Fame ceremony in 2014. Photo by Scott Newton/courtesy ACL and KLRU-TV

Making a documentary of a long-running television show like “Austin City Limits” is probably harder than it might seem on the surface. Sure, you have decades of ready-to-use footage at your disposal. But how do you make it look like something other than a greatest-hits clip show?

Director Keith Maitland — whose other SXSW film this year, “Tower,” won the festival’s documentary jury prize — managed the task by using those archives only sparingly, and when he did, generally focusing on the very best of the very best. Most of “A Song for You: The Austin City Limits Story” gets told from behind-the-scenes footage, some historical and some shot specifically for this film over the past couple of years.

Among the most effective methods was following ACL executive producer Terry Lickona and his crew through a series of meetings to plan the launch of their ACL Hall of Fame two years ago. We get a sense of how such projects come together, sometimes with animated discussion among the staffers, sometimes with Lickona just casually mentioning that he texted Lyle Lovett about performing and got the green light.

Lovett figures prominently in one of the key sections near the end of the film, as he and his Large Band taped the final episode at the show’s historic Studio 6A home before the move downtown to ACL Live in 2011. It’s touching to see Lovett taking time out to talk with the show’s creator, Bill Arhos, just moments before taking the stage.

The relationship between Arhos and Lickona also helps to personalize the film. Lickona, who has steered the show since its fourth season, worked closely with Arhos until the latter’s retirement in 2000. The death of Arhos last year makes their conversations in this film bittersweet, especially set against classic and fittingly minimal footage of Willie Nelson singing the movie’s namesake tune, “A Song for You.”

Dozens of artists from a wide range of genres are interviewed briefly throughout the film, so many that the focus sometimes feels a bit scattershot. The best moments come when the pace slows down, focusing on the musical magic that happens when, say, Thao Nguyen talks to her mom just after taping the show, or when Dolly Parton sings her classic “I Will Always Love You.” As many artists stress, the TV show has succeeded because, in St. Vincent’s words, “it’s not about smoke and mirrors.” The best stretches of “A Song for You” follows that same principle.